text: The Stokes drift was formulated for water waves by George Gabriel Stokes in 1847. For simplicity, the case of infinitely deep water is considered, with linear wave propagation of a sinusoidal wave on the free surface of a fluid layer:
  where
  : η is the elevation of the free surface in the z direction (meters),
  : a is the wave amplitude (meters),
  : k is the wave number: k = 2π/λ (radians per meter),
  : ω is the angular frequency: ω = 2π/T (radians per second),
  : x is the horizontal coordinate and the wave propagation direction (meters),
  : z is the vertical coordinate, with the positive z direction pointing out of the fluid layer (meters),
  : λ is the wave length (meters),
  : T is the wave period (seconds).
  As derived below, the horizontal component ū(z) of the Stokes drift velocity for deep-water waves is approximately:
  As can be seen, the Stokes drift velocity ū is a nonlinear quantity in terms of the wave amplitude a. Further, the Stokes drift velocity decays exponentially with depth: at a depth of a quarter wavelength, z = −λ/4, it is about 4% of its value at the mean free surface, z = 0.